The serial number starts with R171 - not sure who that is. The cog (Shimano SIS 5-Speed) says VC on it, so according to your chart that would be March of 1997. That's not quite as old as I was hoping for, but it's not too new either.

EDIT: Update - My dad doesn't want to return the new Dyna. We talked it over and he said if I fix the old bike, we'll keep the Dyna around as a spare bike that he and my brother can both use, and I'll keep riding the FS. Neither of them are really into bicycles so that works out for them, and it's their bike now, which means I can forget about the Dyna and focus on fixing the FS. I'll be going taking the wheel to my LBS to see it it's fixable ASAP, and if not I'll start looking around on Craigslist and thrift shops for a new one.